Multiplicative Hankel matrices

In two papers, published in 2006 and (posthumously) in 2010, Henry Helson initiated a study of multiplicative Hankel matrices, which are finite or infinite matrices whose entries

\[a_{m,n}\]

only depend on the product

\[m\cdot n\]

. I will discuss the motivation for these papers, their contents, and subsequent developments. In particular, I will give an answer to the following question: What is the multiplicative analogue of the classical Hilbert matrix? Here it will be seen that the Riemann zeta function shows up in a natural way.